Vibration Characteristics of the Non-Conservative Thermoelastic Coupling Plate

2011 ◽  
Vol 66-68 ◽  
pp. 551-556
Author(s):  
X. X. Guo
Keyword(s):  
Rectangular Plate ◽  
Differential Quadrature Method ◽  
Coupling Factor ◽  
Vibration Characteristics ◽  
Follower Force ◽  
Quadrature Method ◽  
Thermoelastic Coupling ◽  
Coupled Modes ◽  
Simply Supported ◽  
The Stability

The vibration characteristics of the thermoelastic coupling rectangular plate under the action of uniformly distributed tangential follower force are investigated. The coupled thermoelastic differential equation of the plate under the action of uniformly distributed tangential follower force was derived. Dimensionless complex frequencies of the thermoelastic coupling rectangular plate with one edge clamped and other three edges simply supported, two opposite edges simply supported and other two edges clamped were calculated by the differential quadrature method. The effects of the dimensionless thermoelastic coupling factor on the stability and critical load of the thin plate were analyzed. The results show that the flutter loads of the coupled modes increase with the increase of the dimensionless coupled thermoelastic factor and the aspect ratio.

Thermoelastic Coupling Vibration of the Moving Rectangular Plate

2013 ◽  
Vol 319 ◽  
pp. 435-439
Author(s):  
Xu Xia Guo
Keyword(s):  
Differential Equation ◽  
Rectangular Plate ◽  
Differential Quadrature Method ◽  
Coupling Factor ◽  
Thermoelastic Coupling ◽  
Coupling Term ◽  
Moving Plate ◽  
Coupling Vibration ◽  
Simply Supported ◽  
Moving Speed

The dynamic characteristics and stability of the thermoelastic coupling moving rectangular plate are investigated. Based on the heat conduction equation involving the thermoelastic coupling term and the differential equation of motion of the plate subjected to the thermal shock, the thermoelastic coupling differential equation of the moving plate is derived. Dimensionless complex frequencies of the thermoelastic coupling moving rectangular plate with two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The results show that the first mode behaves divergent instability firstly, and the critical divergent moving speed of the first mode increase with the increase of the thermoelastic coupling factor for the two kinds of boundary conditions.

scholarly journals Vibration Characteristics for Moving Printing Membrane with Variable Density along the Lateral Direction

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Mingyue Shao ◽  
Jimei Wu ◽  
Yan Wang ◽  
Qiumin Wu ◽  
Yuan Chen
Keyword(s):  
Density Distribution ◽  
Transverse Vibration ◽  
High Speed ◽  
Differential Quadrature Method ◽  
Variable Density ◽  
Vibration Characteristics ◽  
Lateral Direction ◽  
Vibration Model ◽  
The Stability ◽  
Density Coefficient

The vibration model of moving membrane with variable density distribution is established, and the density distribution of the moving membrane varies along the lateral direction. The transverse vibration differential equations of moving membrane are established based on D’Alembert’s principle and discretized by using the differential quadrature method (DQM). The relationships of the first three dimensionless complex frequencies between dimensionless speed, density coefficient, and tension ratio of the membrane are analyzed by numerical calculation. The effects of the density coefficient and the tension ratio on transverse vibration characteristics of the membrane are investigated. The relationship between density coefficient and critical speed is obtained. The numerical results show that the density coefficient and the tension ratio have important influence on the stability of moving membrane. So the study provides a theoretical basis for improving the working stability of the membrane in the high-speed printing process.

Analysis of the vibration of axially moving viscoelastic plate with free edges using differential quadrature method

2017 ◽  
Vol 24 (17) ◽  
pp. 3908-3919 ◽  
Author(s):  
Mouafo Teifouet Armand Robinson
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Viscoelastic Plate ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Simply Supported ◽  
System Parameters ◽  
Complex Eigenvalues ◽  
Axially Moving ◽  
Viscoelastic Rectangular Plate

The two-dimensional viscoelastic differential constitutive relation is employed in this paper, in order to establish the equation of motion of axially moving viscoelastic rectangular plate. Two boundary conditions are investigated, namely the clamped free and two opposite edges simply supported and two others free. The differential quadrature method is used to solve the resulting complex eigenvalues equation. The influence of boundary conditions on the instability of a moving viscoelastic plate is analyzed firstly, and secondly the effects of system parameters such as plate's viscosity and aspect ratio on the vibration frequencies are presented.

Thermoelastic Coupling Vibration Characteristics of the Axially Moving Beam With Frictional Contact

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Guo Xu-Xia ◽  
Wang Zhong-Min
Keyword(s):  
Frictional Contact ◽  
Differential Quadrature Method ◽  
Contact Point ◽  
Normal Pressure ◽  
Vibration Characteristics ◽  
Axially Moving Beam ◽  
Thermoelastic Coupling ◽  
Coupling Vibration ◽  
Moving Beam ◽  
Axially Moving

The thermoelastic coupling vibration characteristics of the axially moving beam with frictional contact are investigated. The piecewise differential equation of motion for the axially moving beam in the thermoelastic coupling case and the continuous conditions at the contact point are established. The eigenequation is derived by the differential quadrature method, and the first order dimensionless complex frequencies of the simply supported axially moving beam under the coupled thermoelastic case are calculated. The effects of the dimensionless thermoelastic coupling factor, the dimensionless moving speed, the spring stiffness, the friction coefficient, and the normal pressure on the thermoelastic coupling vibration characteristics of the axially moving beam with frictional contact are discussed.

A numerical study of two-dimensional coupled systems and higher order partial differential equations

2019 ◽  
Vol 12 (05) ◽  
pp. 1950071
Author(s):  
R. Rohila ◽  
R. C. Mittal
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Differential Quadrature Method ◽  
Bernstein Polynomials ◽  
Differential Quadrature ◽  
Coupled Systems ◽  
Two Dimensional ◽  
Quadrature Method ◽  
Grid Points ◽  
The Stability

In this paper, a new approach and methodology is developed by incorporating differential quadrature technique with Bernstein polynomials. In differential quadrature method, approximations are done in a way that the derivatives of the function are replaced by a linear sum of functional values at the grid points of the given domain. In Bernstein differential quadrature method (BDQM), Bernstein polynomials are employed for spatial discretization so that a system of ordinary differential equations (ODE’s) is obtained which is solved by SSPRK-43 method. The stability of the method is also studied. The accuracy of the present method is checked by performing numerical experiments on two-dimensional coupled Burgers’ and Brusselator systems and fourth-order extended Fisher Kolmogorov (EFK) equation. Implementation of the method is very easy, efficient and capable of reducing the size of computational efforts.

scholarly journals Stability of Axially Moving Piezolaminated Viscoelastic Plate Subjected to Follower Force

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yan Wang ◽  
Tao Jing ◽  
Jimei Wu ◽  
Min Xie
Keyword(s):  
Piezoelectric Layer ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Tensile Force ◽  
Viscoelastic Plate ◽  
Follower Force ◽  
Complex Eigenvalue ◽  
Axially Moving ◽  
The Stability ◽  
Moving Speed

The stability of the moving viscoelastic plate with the piezoelectric layer subjected to uniformly distributed tangential follower force is investigated. The force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force. The differential equation of the axially moving viscoelastic rectangular plate with piezoelectric layer subjected to uniformly distributed tangential follower force is formulated on the basis of the Kirchhoff thin plate theory and the two-dimensional viscoelastic differential constitutive relation. The complex eigenvalue equations are established by the differential quadrature method. Via numerical calculation, the curves of real parts and imaginary parts of dimensionless complex frequencies versus uniformly distributed tangential follower force and dimensionless moving speed are obtained. The effects of nonconservative force, dimensionless axially moving speed, and dimensionless applied voltages on the stability of axially moving nonconservative viscoelastic plate with piezoelectric layer are analyzed.

Fourier Cosine Differential Quadrature Method for Beam and Plate Problems

2011 ◽  
Vol 138-139 ◽  
pp. 699-704 ◽  
Author(s):  
Wen Ting Shao ◽  
Xiong Hua Wu
Keyword(s):  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Engineering Problems ◽  
Complex Boundary ◽  
The Stability ◽  
Barycentric Form

In this paper, we combined the Fourier cosine series and differential quadrature method (DQM) in barycentric form to develop a new method (FCDQM), which is applied to the 1D fourth order beam problem and the 2D thin isotropic plate problems. Furthermore, we solved the complex boundary conditions on irregular domains with DQM directly. The numerical results illustrate the stability, validity and good accuracy of the method in treating this class of engineering problems.

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